What is Euler's Equation of Motion??
EULER’S EQUATION OF MOTION
Consider a streamline in which flow is taking place in s-direction.
Consider a cylindrical element of cross section dA and length ds. The forces actingon the cylindrical element are:
1. Pressure force pdA in the direction of flow
2. Pressure force (p + 𝜕𝑝𝜕𝑠 ds) dA opposite to direction of flow
3. Weight of element 𝜌𝑔𝑑𝐴𝑑𝑠
Let us consider that θ is the angle between the direction of fluid flow and the line of action of weight of the fluid element.
According to Newton’s second law of motion. Net force over the fluid element in the direction of S = Mass of the fluid element x acceleration in the direction S.